Tension members or means such as ropes and cables are subject to oscillations. These members can be excited by external forces such as wind. If the frequency of exciting forces matches the natural frequency of the tension member, then the tension member will resonate.
High velocity winds cause buildings to sway back and forth. The frequency of the building sway can match the natural frequency of the elevator causing resonance. In resonance, the amplitude of the oscillations increases unless limited by some form of dampening. This resonance can cause significant damage to both the elevator system and the structure.
Two major problems plague high rise elevators with long hoist ropes and correspondingly long compensation ropes. These are rope sway and re-leveling due to rope elongation. Rope sway, particularly compensation rope sway, is a major problem in high rise buildings.
The fundamental frequency (also called natural frequency) of a periodic signal is the inverse of the pitch period length. The pitch period is, in turn, the smallest repeating unit of a signal. The significance of defining the pitch period as the smallest repeating unit can be appreciated by noting that two or more concatenated pitch periods form a repeating pattern in the signal. In mechanical applications a tension member, such as a suspension rope, fixed at one end and having a mass attached to the other, is a single degree of freedom oscillator. Once set into motion, it will oscillate at its natural frequency. For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties; mass and stiffness. Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations of an oscillatory system.
Because of a low mass of a compensation sheave around which a compensation rope is wound, the natural frequency of the compensation ropes is very low and is normally between 0.05 Hz and 1 Hz. The following equation (Equation 1) can used be to calculate the natural frequency of compensation ropes in Hz:
                              f          n                =                              n                          2              ⁢              L                                ⁢                                    g              ⁡                              (                                                      M                                          2                      ⁢                                              n                        c                                            ⁢                      m                                                        +                                      L                    2                                                  )                                                                        (        1        )            where g=9.81 m/s2 is the acceleration of gravity, n denotes the vibration mode number, nC is the number of ropes, L is the length of the rope (in m), M represents mass of the compensating sheave assembly (in kg), and m is mass of the rope per unit length (in kg/m).
High rise buildings are known to sway during windy conditions. The frequency of the building sway is generally between 0.05 and 1 Hz. Because the natural frequency of the compensation ropes is very close to the natural frequency of the building, resonance often occurs. Compensation rope resonance can cause the ropes to strike the walls and elevator doors causing damage and frightening passengers.
The U.S. Pat. No. 8,123,002 B2 discloses a system and method for minimizing compensation rope sway by altering the natural frequency of compensation ropes using servo actuators. The rope sway is minimized by moving the compensation sheave of the compensation rope to modulate tension of the compensation rope or to adjust the position of the termination of a compensation rope to account for changes in the position of a structure.